Nonlinear Forecast Error Variance Decompositions: Shapley Shares, Generalized Shapley Shares, and the Role of Structural Interactions

Forecast error variance decompositions (FEVDs) are widely used to assess the contribution of structural shocks in vector autoregressions. However, many variables of interest are nonlinear functions of underlying variables, rendering the standard linear FEVD incomplete. We develop a framework for variance decomposition of nonlinear forecast targets in terms of the Shapley value decomposition and compare it with more conventional approaches based on Taylor expansions. We illustrate that nonlinear interaction effects can account for components of forecast uncertainty that are not fully captured by Taylor approximations. As a result, approximation-based FEVD may substantially distort the picture of forecast uncertainty and the attribution of variance across shocks.